Martians

A sphere-shaped spaceship with a diameter of 6 m landed in the meadow. To avoid attracting attention, the Martians covered it with a roof in the shape of a regular cone. How high will this roof be so that the consumption of roofing is minimal?

Correct answer:

S =  115.6965 m2

Step-by-step explanation:

D=6 m R=D/2=6/2=3 m  sin α = r / s   R : (hR) = r : s = sin α   r = s   hRR  S = π r s = π    R / (hR)   s2  S = π    R / (hR)   (( R / (hR))2+h2)  S = (3 (9/(3 + h)2 + h2) π)/(3 + h)  h=6.372526.3725 m  s=(R/(hR))2+h2=(3/(6.37253))2+6.372526.4343 m r=s hRR=6.4343 6.3725335.7236 m  S=π r s=3.1416 5.7236 6.4343=115.6965 m2



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